Heartbeat

Heartbeat is a long running British drama series set in rural Yorkshire in The Sixties, about the adventures of the local constabulary and medical services of the village of Aidensfield and the larger town of Ashfordly where the main police station of the area is situated.

The series originally began with Constable Nick Rowan and his doctor wife accepting a reassignment from London, which was troubled with considerable civil unrest at the time. As Rowan and comrades keep the peace, they keep a wary eye for the local con man, Claude Greengrass, who is forever looking for the next big score, which is usually just this side of legal to keep them from arresting him.

The series feels much like a police version of All Creatures Great and Small (Johnny Byrne was effectively the showrunner for both series) as small town life proves incredibly lively with numerous crimes to solve and medical problems to treat, usually with a touch of humour.

Tropes used in Heartbeat include:

Actor Allusion - expect some very knowing dialogue whenever the guest star is anybody famous for something other than acting.
Bottle Episode - One Small Step (aka "the one where they all watch the moon landing").
Characterization Marches On - Although it's meant to be the same character, David Stockwell's debut as a mentally handicapped man barely capable of doing anything for himself bears very little resemblance to his subsequent goofy but normally-functioning characterization when brought back as a regular.
Comic Trio
Cryptid Episode: In one episode, the cops go searching for some legendary big cats that are killing sheep on the Yorkshire moors. They turn out to be incompetent sheep rustlers instead.
Dropped a Bridge on Him - About 90% of the show's main character deaths.
Fake Defector
Faking the Dead - Vernon Scripps, twice.
A Father to His Men - Blaketon, starts becoming this in Series 3/4.
Four-Temperament Ensemble
Friendly Enemy - One of the main character development arcs in the early series is how Rowan and Greengrass' relationship mellows into this.
"Friend or Idol?" Decision
Frozen in Time - 18 seasons and the series remained firmly in the 1960s. In fact, it was specifically 1969 long enough that one character had two full term pregnancies in that year...
Get Rich Quick Scheme - Vernon Scripps' favoured way of making a living.
The Ghost - Mrs. Ventress.
The Grim Reaper - wanders around in the background shortly before Oscar Blaketon cops it.
I Am Spartacus
Loveable Rogue
New Neighbours as the Plot Demands
One Steve Limit - Literally averted: When the show introduced PC Steve Crane, they apparently forgot that supporting character Jenny Latimer had a brother called Steve and they ended up appearing in the same episode.
Overtook the Series - already a very loose adaptation of Nicholas Rhea' source novels, the show quickly went its own way.
Playing Against Type: Gwen Taylor took the role of Peggy Armstrong as it gave her an opportunity to play a nasty character for once. She later expressed disappointment at Peggy being softened up in her second season.
Real Song Theme Tune - "Heartbeat", originally a hit for Buddy Holly which charted in the UK in 1959 and 1960. The TV series used a cover version sung by the actor who played Nick Rowan.
Train Job
Sitcom Arch Nemesis - From the famous words of Sargent Blaketon, "Greengrass!"
Wrench Wench - Rosie